document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262848>Question 262848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the formula h=vt-16t^2 gives the height h in feet of an object after t sec. Here v is the initial velocity of the object expressed in feet per second. suppose a toy rocket was launched from the ground straight up with an initial velocity of 64ft/sec. How many seconds after launch was the rocket 48 ft above the ground.\r<BR>\n" );
document.write( "\n" );
document.write( "ok so here is what i have so far:<BR>\n" );
document.write( "using the formula and what is given i have   48=64t-16t^2 so i need to make it a quadratic like this 64t-16t^2-48=0  then multiply by -1 and put it in the correct order i get:<BR>\n" );
document.write( "16t^2-64t+48=0<BR>\n" );
document.write( "16(t^2-4t+3)=0<BR>\n" );
document.write( "16(t-3)(t-1)<BR>\n" );
document.write( "so i get two positive answers. when i put t=1 into the formula like this:<BR>\n" );
document.write( "48=64(1)-16(1^2) I get<BR>\n" );
document.write( "48=48<BR>\n" );
document.write( "but how can something launched at 64ft per second only be 48 feet up after 1 second?  is my answer wrong or am i missing something in the physics of the problem?<BR>\n" );
document.write( "i hope my notation is clear. any help you can give would be appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193627 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula h=vt-16t^2 gives the height h in feet of an object after t sec. Here v is the initial velocity of the object expressed in feet per second. suppose a toy rocket was launched from the ground straight up with an initial velocity of 64ft/sec. How many seconds after launch was the rocket 48 ft above the ground. <BR>\n" );
document.write( "ok so here is what i have so far:<BR>\n" );
document.write( "using the formula and what is given i have 48=64t-16t^2 so i need to make it a quadratic like this 64t-16t^2-48=0 then multiply by -1 and put it in the correct order i get:<BR>\n" );
document.write( "16t^2-64t+48=0<BR>\n" );
document.write( "16(t^2-4t+3)=0<BR>\n" );
document.write( "16(t-3)(t-1)<BR>\n" );
document.write( "so i get two positive answers. when i put t=1 into the formula like this:<BR>\n" );
document.write( "48=64(1)-16(1^2) I get<BR>\n" );
document.write( "48=48<BR>\n" );
document.write( "but how can something launched at 64ft per second only be 48 feet up after 1 second? is my answer wrong or am i missing something in the physics of the problem?<BR>\n" );
document.write( "i hope my notation is clear. any help you can give would be appreciated. <BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "the formula h=vt-16t^2 gives the height h in feet of an object after t sec. Here v is the initial velocity of the object expressed in feet per second. suppose a toy rocket was launched from the ground straight up with an initial velocity of 64ft/sec. How many seconds after launch was the rocket 48 ft above the ground. <BR>\n" );
document.write( "ok so here is what i have so far:<BR>\n" );
document.write( "using the formula and what is given i have 48=64t-16t^2 so i need to make it a quadratic like this 64t-16t^2-48=0 then multiply by -1 and put it in the correct order i get:<BR>\n" );
document.write( "16t^2-64t+48=0<BR>\n" );
document.write( "16(t^2-4t+3)=0<BR>\n" );
document.write( "16(t-3)(t-1)<BR>\n" );
document.write( "so i get two positive answers. when i put t=1 into the formula like this:<BR>\n" );
document.write( "48=64(1)-16(1^2) I get<BR>\n" );
document.write( "48=48<BR>\n" );
document.write( "but how can something launched at 64ft per second only be 48 feet up after 1 second? is my answer wrong or am i missing something in the physics of the problem?<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Ans: Gravity is pulling the object back to earth at the rate of 16 ft.<BR>\n" );
document.write( "per second<BR>\n" );
document.write( "------------------------------------------------------------------------<BR>\n" );
document.write( "I hope my notation is clear. any help you can give would be appreciated. <BR>\n" );
document.write( "the formula h(t) = vt-16t^2 gives the height h in feet of an object after t sec.<BR>\n" );
document.write( "How many seconds after launch was the rocket 48 ft above the ground.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-16t^2 + 64t = 48<BR>\n" );
document.write( "-16t^2 + 64t - 48 = 0<BR>\n" );
document.write( "-16(t^2 - 4t + 3) = 0<BR>\n" );
document.write( "t^2 - 4t + 3 = 0<BR>\n" );
document.write( "(t-3)(t-1) = 0<BR>\n" );
document.write( "t = 1 second ; t = 3 seconds<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-5%2C5%2C-5%2C70%2C-16x%5E2%2B64x%2C48%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-5%2C5%2C-5%2C70%2C-16x%5E2%2B64x%2C48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );